6533b7d5fe1ef96bd1263c94
RESEARCH PRODUCT
Shape optimization for monge-ampére equations via domain derivative
Barbara BrandoliniCristina TrombettiCarlo Nitschsubject
Dirichlet problemMathematical optimizationPure mathematicsFictitious domain methodDomain derivativeApplied MathematicsOpen setRegular polygonMonge–Ampère equationMonge-Ampère equationSettore MAT/05 - Analisi MatematicaGeneralizations of the derivativeNorm (mathematics)Discrete Mathematics and CombinatoricsAffine isoperimetric inequalitiesConvex functionAnalysisMathematicsdescription
In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 |